Bézier curves code

Coding Python Support
1

Here’s the code for manually interpolating between points using Bézier’s equations if anyone’s interested. You can easily use this to generate a curvy mesh with a custom resolution…

The view the second posting for updated code

import Blender
from Blender import NMesh 
from math import pow


def Bezier3(p1,p2,p3,mu):
	#_________________________________________
	#Three control point Bezier interpolation
	#Parameters: p1 to p3- 3 point tuple [x,y,z]
	#mu ranges from 0 to 1 (start to end of curve) 
	#_________________________________________
	p = [0,0,0]

	mu2 = mu * mu
	mum1 = 1 - mu
	mum12 = mum1 * mum1
 	for z in range(3):  
		p[z] = p1[z] * mum12 + 2 * p2[z] * mum1 * mu + p3[z] * mu2

	return(p);


def Bezier4(p1,p2,p3,p4,mu):
	#_________________________________________
	#Four control point Bezier interpolation
	#Parameters: p1 to p4- 3 point tuple [x,y,z]
	#mu ranges from 0 to 1 (start to end of curve) 
	#_________________________________________
	p = [0,0,0]
	mum1 = 1 - mu
	mum13 = mum1 * mum1 * mum1
	mu3 = mu * mu * mu

	for z in range(3):
		p[z] = mum13*p1[z] + 3*mu*mum1*mum1*p2[z] + 3*mu*mu*mum1*p3[z] + mu3*p4[z]
	return(p)
   
def Bezier(p,mu):
	#_________________________________________
	#General Bezier curve
	#Parameters: p array of points ( etc [[x1,y1,z1],[x2,y2,z2],...] )
	#mu ranges from 0 to 1 (start to end of curve)
	#_________________________________________
	b = [0,0,0]
	n = len(p)
	muk = 1
	munk = pow(1-mu,n)

	
	for k in range(n):  
		nn = n
		kn = k
		nkn = n - k
		blend = muk * munk
		muk *= mu
		munk /= (1-mu)
		while nn >= 1:
			blend *= nn
			nn -=1
			if kn > 1:
				blend /= float(kn)
				kn-=1
			if nkn > 1:
				blend /= float(nkn)
				nkn-=1
  		for z in range(3):    
			b[z] += p[k][z] * blend
	return(b)

me = NMesh.GetRaw()

verts = [[8,-1,-20],[-9,2,8],[10,36,-3],[8,8,8],[10,4,-10],[0,0,0],[10,10,2]]

points = 300

for y in range(points):
	#vertex = Bezier3(verts[1],verts[2],verts[3], float(y)/s)
	#vertex = Bezier4(verts[1],verts[2],verts[3],verts[4], float(y)/s)
	vertex = Bezier(verts,float(y)/s)
	vert = NMesh.Vert(vertex[0],vertex[1],vertex[2])
	me.verts.append(vert)

NMesh.PutRaw(me)
2

There was an error in the general Bézier function that made the last point go towards [0,0,0]. The following line needed to be inserted before munk was defined:

mu *= (.4*pow(len(p),.15))

So the functions should now read:

import Blender 
from Blender import NMesh 
from math import pow 


def Bezier3(p1,p2,p3,mu): 
   #_________________________________________ 
   #Three control point Bezier interpolation 
   #Parameters: p1 to p3- 3 point tuple [x,y,z] 
   #mu ranges from 0 to 1 (start to end of curve) 
   #_________________________________________ 
   p = [0,0,0] 

   mu2 = mu * mu 
   mum1 = 1 - mu 
   mum12 = mum1 * mum1 
   for z in range(3):  
      p[z] = p1[z] * mum12 + 2 * p2[z] * mum1 * mu + p3[z] * mu2 

   return(p); 


def Bezier4(p1,p2,p3,p4,mu): 
   #_________________________________________ 
   #Four control point Bezier interpolation 
   #Parameters: p1 to p4- 3 point tuple [x,y,z] 
   #mu ranges from 0 to 1 (start to end of curve) 
   #_________________________________________ 
   p = [0,0,0] 
   mum1 = 1 - mu 
   mum13 = mum1 * mum1 * mum1 
   mu3 = mu * mu * mu 

   for z in range(3): 
      p[z] = mum13*p1[z] + 3*mu*mum1*mum1*p2[z] + 3*mu*mu*mum1*p3[z] + mu3*p4[z] 
   return(p) 
    
def Bezier(p,mu): 
   #_________________________________________ 
   #General Bezier curve 
   #Parameters: p array of points ( etc [[x1,y1,z1],[x2,y2,z2],...] ) 
   #mu ranges from 0 to 1 (start to end of curve) 
   #IMPORTANT, the last point is not computed 
   #_________________________________________ 
   b = [0,0,0] 
   n = len(p) 
   muk = 1 
   mu *= (.4*pow(len(p),.15)) 
   munk = pow(1-mu,n) 
    

    
   for k in range(n):  
      nn = n 
      kn = k 
      nkn = n - k 
      blend = muk * munk 
      muk *= mu 
      munk /= (1-mu) 
      while nn >= 1: 
         blend *= nn 
         nn -=1 
         if kn > 1: 
            blend /= float(kn) 
            kn-=1 
         if nkn > 1: 
            blend /= float(nkn) 
            nkn-=1 
      for z in range(3):
          b[z] += p[k][z] * blend 
   return(b) 

me = NMesh.GetRaw() 

verts = [[8,-1,-20],[-9,2,8],[10,36,-3],[8,8,8],[10,4,-10],[0,0,0],[10,10,2]] 

points = 30 

for y in range(points): 
   #vertex = Bezier3(verts[1],verts[2],verts[3], float(y)/s) 
   #vertex = Bezier4(verts[1],verts[2],verts[3],verts[4], float(y)/s) 
   vertex = Bezier(verts,float(y)/points) 
   vert = NMesh.Vert(vertex[0],vertex[1],vertex[2]) 
   me.verts.append(vert) 

NMesh.PutRaw(me)
3

Thank you.